Newton-Krylov methods applied to nonequilibrium radiation diffusion

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The authors present results of applying a matrix-free Newton-Krylov method to a nonequilibrium radiation diffusion problem. Here, there is no use of operator splitting, and Newton`s method is used to convert the nonlinearities within a time step. Since the nonlinear residual is formed, it is used to monitor convergence. It is demonstrated that a simple Picard-based linearization produces a sufficient preconditioning matrix for the Krylov method, thus elevating the need to form or store a Jacobian matrix for Newton`s method. They discuss the possibility that the Newton-Krylov approach may allow larger time steps, without loss of accuracy, as compared to ... continued below

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6 p.

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Knoll, D. A.; Rider, W. J. & Olsen, G. L. March 10, 1998.

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  • Los Alamos National Laboratory
    Publisher Info: Los Alamos National Lab., Applied Theoretical and Computational Physics Div., NM (United States)
    Place of Publication: New Mexico

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Description

The authors present results of applying a matrix-free Newton-Krylov method to a nonequilibrium radiation diffusion problem. Here, there is no use of operator splitting, and Newton`s method is used to convert the nonlinearities within a time step. Since the nonlinear residual is formed, it is used to monitor convergence. It is demonstrated that a simple Picard-based linearization produces a sufficient preconditioning matrix for the Krylov method, thus elevating the need to form or store a Jacobian matrix for Newton`s method. They discuss the possibility that the Newton-Krylov approach may allow larger time steps, without loss of accuracy, as compared to an operator split approach where nonlinearities are not converged within a time step.

Physical Description

6 p.

Notes

INIS; OSTI as DE98006340

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  • 5. Copper Mountain conference on iterative methods, Copper Mountain, CO (United States), 30 Mar - 3 Apr 1998

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  • Other: DE98006340
  • Report No.: LA-UR--98-1076
  • Report No.: CONF-980393--
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 666037
  • Archival Resource Key: ark:/67531/metadc712560

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  • March 10, 1998

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  • Sept. 12, 2015, 6:31 a.m.

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  • Nov. 3, 2016, 1:30 p.m.

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Knoll, D. A.; Rider, W. J. & Olsen, G. L. Newton-Krylov methods applied to nonequilibrium radiation diffusion, article, March 10, 1998; New Mexico. (digital.library.unt.edu/ark:/67531/metadc712560/: accessed December 14, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.